Q. 1 F5.0( 2 Votes )

# Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion.

Answer :

Given rational number is

is terminating if

a) p and q are co-prime &

b) q is of the form of 2^{n} 5^{m} where n and m are non-negative integers.

__Firstly, we check co-prime__

7 = 7 × 1

80 = 2 × 2 × 2 × 2 × 5

7 and 80 have no common factors

Therefore, 7 and 80 are co-prime.

Now, we have to check that q is in the form of 2^{n}5^{m}

80 = 2^{4} × 5

So, denominator is of the form 2^{n}5^{m} where n = 4 and m = 1

Thus, is a **terminating** decimal.

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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating

(i) (ii)

(iii) (iv)

(v)

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